The profinite completion of a group localised at a subgroup

Abstract

Let $G$ be a group and let $K$ be a commensurated subgroup of $G$. Then there is a totally disconnected, locally compact (t.d.l.c.) group ${\hat{G}}_K$ that contains the profinite completion of $K$ as an open compact subgroup and also contains $G$ (modulo the finite residual of $K$) as a dense subgroup. Moreover, given an arbitrary group $G$, then every t.d.l.c. group containing an image of $G$ as a dense subgroup can be realised as a quotient of ${\hat{G}}_K$ for some commensurated subgroup $K$.

Superseded by http://arxiv.org/abs/1509.00156

References in corpus (1)

• Some aspects of profinite group theory

Cited by in corpus (2)

• Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups
• Locally normal subgroups of totally disconnected groups. Part I: General theory